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1. If total cost is given by TC = 10Q −5Q²+ 0.1Q³, where Q is the level of output.

(1). Obtain the marginal cost function.

(2). What is the output level so the marginal cost is minimized?

(3). Obtain the average cost function.

(4). What is the output level so the average cost is minimized?

2. Trudeau’s Body Shop incurs total costs given by TC = 2,400 + 100Q. If the price it charges for a paint job is $120, what is its break- even level of output?

 

3.A representative firm with short- run total cost given by TC = 20 + 20q + 5q² operates in a competitive industry where the short- run market demand and supply curves are given by Q_D = 1,400 −40P and Q_S = −400 + 20P.
(1). If the firm is perfectly competitive, what is the optimum output rate?

(2). At this output rate, what is the profit?

 

4.If a representative firm with long-run total cost given by TC = 400 + 45Q – 8Q2 + 0.7Q3 operates in a competitive industry, at what price level, will this firm shutdown in the short run?

5. Craig’s Red Sea Restaurant is the only restaurant in Columbia, South Carolina, that sells Ethiopian food. The demand for Ethiopian food is given by Q = 10,000 – 20P. Craig’s costs are given by TC = 1,000 + 10Q + .05Q2.

(1). If Craig behaves like a monopolist, what are the output level and price to maximize its profit?

(2). If Craig behaves like a purely competitive firm, what are the output level and price to maximize its profit?

 

6. If Harry Doubleday’s price elasticity of demand is −0.1, and its profit maximizing price is $8, what is its marginal cost?

 

7. A monopolist sells to two consumer groups, students and non-students.

        Demand for students: Q = 500 – 0.5P

        Demand for non-students: Q = 750 – 2P

        MC = 20

Find the profit-maximizing price/quantity combination in each market if the groups can be separated.

8. If a firm supplies separable markets with price elasticities −4 and −3, what is the relationship between P₁ and P₂ ?

 

Two local ready- mix cement manufacturers, Here and There, have combined demand given by Q = 10 –P, where  Q=Q₁+Q₂. Their total costs are given by TC₁= 5 + Q²₁ and TC₂ = 5 + Q²₂.

(1). If they engage in price competition, what is the equilibrium price? What is the output of each firm?

 

(2). If they successfully collude, what is the equilibrium price? What is the output of each firm?
(3). If managers at these two firms set their own output levels to maximize profit, assuming that managers at the other firm hold constant their output, what is the equilibrium price? What is the output of each firm? How much profit do managers at each firm earn?